# How do you solve the system #-x-5y-5z=2#, #4x-5y+4z=19#, and #x+5y-z=-20#?

##### 1 Answer

#### Answer:

Verify that the determinant of the coefficient matrix is not zero.

If so, then create and augmented matrix by appending of column of constants.

Perform elementary row operations, until solved.

#### Explanation:

Let A equal the coefficient matrix :

Verify that the determinant is not zero:

NOTE: I wrote all of the steps to compute the determinant but it made the write up too long. Please read the reference link. The determinant is not zero, therefore there is a unique solution.

Let B = the column of constants:

Write augmented matrix by appending B to A:

Perform elementary row operations until the left is an identity matrix :

We have an identity matrix on the left, therefore, the right contains the values of the variables:

check:

This checks.